Solve (5^{-1})^{-2}*(2^{4}*5^7)div(2^2*5^2^5)

$$( 5 ^ { - 1 } ) ^ { - 2 } \times ( 2 ^ { 4 } \cdot 5 ^ { 7 } ) \div ( 2 ^ { 2 } \cdot 5 ^ { 2 ^ { 5 } } )$$

Evaluate

$$\frac{4}{11920928955078125}=3.3554432 \cdot 10^{-16}$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply -1 and -2 to get 2.

$$\frac{5^{2}\times 2^{4}\times 5^{7}}{2^{2}\times 5^{2^{5}}}$$

To multiply powers of the same base, add their exponents. Add 2 and 7 to get 9.

$$\frac{5^{9}\times 2^{4}}{2^{2}\times 5^{2^{5}}}$$

Cancel out 2^{2} in both numerator and denominator.

$$\frac{2^{2}\times 5^{9}}{5^{2^{5}}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{4\times 5^{9}}{5^{2^{5}}}$$

Calculate 5 to the power of 9 and get 1953125.

$$\frac{4\times 1953125}{5^{2^{5}}}$$

Multiply 4 and 1953125 to get 7812500.

$$\frac{7812500}{5^{2^{5}}}$$

Calculate 2 to the power of 5 and get 32.

$$\frac{7812500}{5^{32}}$$

Calculate 5 to the power of 32 and get 23283064365386962890625.

$$\frac{7812500}{23283064365386962890625}$$

Reduce the fraction \frac{7812500}{23283064365386962890625} to lowest terms by extracting and canceling out 1953125.

$$\frac{4}{11920928955078125}$$

Factor

$$\frac{2 ^ {2}}{5 ^ {23}} = 3.3554432000000003 \times 10^{-16}$$